Stable Centres II: Finite Classical Groups

Abstract

Farahat and Higman constructed an algebra $\mathrm{FH}$ interpolating the centres of symmetric group algebras $Z(\mathbb{Z}{S}_n)$ by proving that the structure constants in these rings are "polynomial in $n$". Inspired by a construction of $\mathrm{FH}$ due to Ivanov and Kerov, we prove for $G_n=G{L}_n,U_n,S{p}_{2n},O_n$, that the structure constants of $Z(\mathbb{Z}{G}_n({\mathbb{F}}_q))$ are "polynomial in $q^n$", allowing us to construct an equivalent of the Farahat-Higman algebra in each case.

38 pages

References in corpus (1)

• Stable Centres I: Wreath Products